The patterns of permutations

@article{Wilf2002ThePO,
  title={The patterns of permutations},
  author={Herbert S. Wilf},
  journal={Discrete Mathematics},
  year={2002},
  volume={257},
  pages={575-583}
}
Let n, k be positive integers, with k ≤ n, and let τ be a fixed permutation of {1, . . . , k}. We will call τ the pattern. We will look for the pattern τ in permutations σ of n letters. A pattern τ is said to occur in a permutation σ if there are integers 1 ≤ i1 < i2 < . . . < ik ≤ n such that for all 1 ≤ r < s ≤ k we have τ(r) < τ(s) if and only if σ(ir) < σ(is). Example: Suppose τ = (132). Then this pattern of k = 3 letters occurs several times in the following permutation σ, of n = 14… CONTINUE READING

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